How to integrate (e^x)/(1+e^x)?

To integrate (e^x)/(1+e^x), use substitution u = 1+e^x and simplify.

To integrate (e^x)/(1+e^x), use substitution u = 1+e^x. Then, du/dx = e^x and dx = du/e^x. Substituting these into the integral gives:

∫(e^x)/(1+e^x) dx = ∫(1/u) du

Integrating this gives:

= ln|u| + C

Substituting back in for u gives:

= ln|1+e^x| + C

Therefore, the integral of (e^x)/(1+e^x) is ln|1+e^x| + C.